Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Tree Painting

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a tree (an undirected connected acyclic graph) consisting of $$$n$$$ vertices. You are playing a game on this tree.

Initially all vertices are white. On the first turn of the game you choose one vertex and paint it black. Then on each turn you choose a white vertex adjacent (connected by an edge) to any black vertex and paint it black.

Each time when you choose a vertex (even during the first turn), you gain the number of points equal to the size of the connected component consisting only of white vertices that contains the chosen vertex. The game ends when all vertices are painted black.

Let's see the following example:

Vertices $$$1$$$ and $$$4$$$ are painted black already. If you choose the vertex $$$2$$$, you will gain $$$4$$$ points for the connected component consisting of vertices $$$2, 3, 5$$$ and $$$6$$$. If you choose the vertex $$$9$$$, you will gain $$$3$$$ points for the connected component consisting of vertices $$$7, 8$$$ and $$$9$$$.

Your task is to maximize the number of points you gain.

Input

The first line contains an integer $$$n$$$ — the number of vertices in the tree ($$$2 \le n \le 2 \cdot 10^5$$$).

Each of the next $$$n - 1$$$ lines describes an edge of the tree. Edge $$$i$$$ is denoted by two integers $$$u_i$$$ and $$$v_i$$$, the indices of vertices it connects ($$$1 \le u_i, v_i \le n$$$, $$$u_i \ne v_i$$$).

It is guaranteed that the given edges form a tree.

Output

Print one integer — the maximum number of points you gain if you will play optimally.

Examples

Input

9 1 2 2 3 2 5 2 6 1 4 4 9 9 7 9 8

Output

36

Input

5 1 2 1 3 2 4 2 5

Output

14

Note

The first example tree is shown in the problem statement.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/18/2019 23:31:21 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|